Escribe, en tu cuaderno, la letra de la respuesta correcta perteneciente a cada literal. Observa la palabra que se forma.
a) $[(2)^2]^{-1}$
P. 16
b) $\left\{\left[\left(\frac{122}{15}\right)^5\right]^0\right\}^{-3}=$
c) $(0,9)^{15} \div(0,9)^{12}$
T. 2
d) $[4]^2$
E. $\frac{1}{16^3}$
e) $\left[\frac{\left(4^2\right)^{-1}}{16^{-2}}\right]^{-3}$
s. $\left(\frac{9}{10}\right)^3$
-. $\frac{5}{2}
Answer (2)
Evaluate each expression using exponent rules.
Match the result of each expression to the given options.
Write the letters corresponding to the correct answers in order.
The word formed by the letters is \boxed{TSPE}.
Explanation
Introduction Let's evaluate each expression step by step and match the result with the given options to form a word.
Evaluating Expression a a) [ ( 2 ) 2 ] − 1 = ( 4 ) − 1 = 4 1 = 0.25 . The corresponding answer from the list is '-'.
Evaluating Expression b b) { [ ( 15 122 ) 5 ] 0 } − 3 = ( 1 ) − 3 = 1 . The corresponding answer from the list is 'T'.
Evaluating Expression c c) ( 0 , 9 ) 15 ÷ ( 0 , 9 ) 12 = ( 0.9 ) 15 − 12 = ( 0.9 ) 3 = 0.729 = ( 10 9 ) 3 . The corresponding answer from the list is 'S'.
Evaluating Expression d d) [ 4 ] 2 = 4 2 = 16 . The corresponding answer from the list is 'P'.
Evaluating Expression e e) [ 1 6 − 2 ( 4 2 ) − 1 ] − 3 = [ 1 6 − 2 1 6 − 1 ] − 3 = [ 1 6 − 1 − ( − 2 ) ] − 3 = [ 1 6 1 ] − 3 = 1 6 − 3 = 1 6 3 1 . The corresponding answer from the list is 'E'.
Forming the Word Now, let's write down the letters corresponding to the correct answers in the order a, b, c, d, e: -, T, S, P, E. The word formed is 'TSPE'.
Matching Results with Options However, the options provided for the answers are P, T, E, S, and -. So, let's match the results with the options: a) [ ( 2 ) 2 ] − 1 = 4 1 = 0.25 corresponds to '-' b) { [ ( 15 122 ) 5 ] 0 } − 3 = 1 corresponds to 'T' c) ( 0 , 9 ) 15 ÷ ( 0 , 9 ) 12 = ( 0.9 ) 3 = ( 10 9 ) 3 corresponds to 'S' d) [ 4 ] 2 = 16 corresponds to 'P' e) [ 1 6 − 2 ( 4 2 ) − 1 ] − 3 = 1 6 3 1 corresponds to 'E'
So the correct order of letters is -, T, S, P, E.
Examples
Understanding exponents and their properties is crucial in various fields, such as calculating compound interest, determining the growth rate of populations, or even in physics when dealing with exponential decay of radioactive substances. For instance, if you invest 1000 a t anann u a l in t eres t r a t eo f 5 A = 1000(1 + 0.05)^t$. This involves understanding exponents and how they affect the final amount, demonstrating a practical application of these mathematical concepts.
The expressions were evaluated step by step leading to the letters '-', 'T', 'S', 'P', and 'E'. The word formed from these letters is 'TSPE'. Each evaluation corresponds to exponent rules and properties.
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